# Worksheet: Centering in Cubic Lattices

In this worksheet, we will practice describing the atomic coordinates, packing densities, and hole geometries in cubic lattices.

Q1:

What is the coordination number of a cobalt atom in the hexagonal close-packed structure of cobalt metal?

Q2:

What is the coordination number of a chromium atom in the body-centered cubic structure of chromium metal?

Q3:

A unit cell contains equivalent atoms at , , , , , , , , and . Which letter denotes the type of centering displayed by this unit cell?

• AP
• BI
• CC
• DF
• ER

Q4:

The compound contains a metal ion with an ionic radius 49% smaller than that of the anion . Determine which of the following statements is false, given that the metal ions have the following coordinates:

• AThe metal ions are hexacoordinate.
• BThe lattice has a body-centered structure.
• CThe lattice adopts the cubic structure with the highest packing efficiency.
• DThere are four ions within the unit cell.

Q5:

For a face-centered cubic crystal system MX, the metal M is located at the coordinates (1/2, 1/2, 1/2). What would you expect the metal’s coordination number to be?

Q6:

Cesium and sodium are group 1 metals, but the coordination number of cesium in the unit cell is 8, whereas the coordination number of sodium in the unit cell is 6. What allows cesium to have a larger coordination number?

• AChlorine is too electronegative to be completely compatible with sodium.
• BThe radius ratio is greater than that of , forcing anions farther from the metal cation.
• CSodium has a larger ionic radius than cesium, allowing for less anion attraction.
• DDue to its size, cesium makes more contact with adjacent anions than sodium does.

Q7:

Fill in the blanks: The coordination numbers of and in fluorite are and respectively.

• A6, 4
• B4, 2
• C4, 4
• D2, 4
• E4, 6

Q8:

Fill in the blank: Atoms in a body-centered cubic unit cell have a coordination number of .